Description
Paraxial sphero-cylinder meridian power S+C*sin²(theta-axis) in radians, without a prescription recommendation.
Vision research uses stimulus angles, chart notations, image scales, viewing distances, coordinate origins, and observation windows. These quantities have different denominators and measurement conventions. A conversion or support share does not independently establish a visual measurement or its clinical interpretation.
Paraxial sphero-cylinder meridian power S+C*sin²(theta-axis) in radians, without a prescription recommendation.
When to use this tool
Use Astigmatic Power One Meridian Term when you need this image, stimulus, notation, coordinate, or observation component for supplied research data.
How to use the tool and how it works
- Enter sphereDiopters, cylinderDiopters, axisRadians, meridianRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read meridianPower. Use the output convention below.
Return meridianPower=sphereDiopters+cylinderDiopters*sin(meridianRadians-axisRadians)^2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sphereDiopters | Sphere Diopters | Required. Finite number. |
| cylinderDiopters | Cylinder Diopters | Required. Finite number. |
| axisRadians | Cylinder axis in the same radian convention. | Required. Finite number. |
| meridianRadians | Meridian angle in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| meridianPower | Meridian Power | Required. Finite number. |
{
"input": {
"sphereDiopters": -2,
"cylinderDiopters": -1,
"axisRadians": 0,
"meridianRadians": 1.5707963267948966
},
"output": {
"meridianPower": -3
}
}Limitations and assumptions
- Powers use diopters and angles radians in the same meridian convention. This is the ideal sphero-cylindrical meridional-power relation; no prescription validation, vertex correction, complex lens optics, or clinical recommendation is performed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use calibrated acquisition and a documented visual or imaging protocol for complete interpretation. Confirm the reporting notation, viewing geometry, image scale, and support of the underlying observations.
References
Similar or alternative tools
- Prism Power Decentration Prentice Term
Prentice thin-lens prism product with millimeters converted to centimeters; sign follows the supplied lens power and displacement, without patient base-direction assignment.
- Lens Transposition Cylinder Axis Wrap
Algebraic sphero-cylinder transposition with axis normalized to [0,180), not a prescription recommendation.